Stable Mappings and Their Singularities:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer US
1973
|
| Schriftenreihe: | Graduate Texts in Mathematics
14 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book aims to present to first and second year graduate students a beautiful and relatively accessible field of mathematics-the theory of singu larities of stable differentiable mappings. The study of stable singularities is based on the now classical theories of Hassler Whitney, who determined the generic singularities (or lack of them) of Rn ~ Rm (m ~ 2n - 1) and R2 ~ R2, and Marston Morse, for mappings who studied these singularities for Rn ~ R. It was Rene Thorn who noticed (in the late '50's) that all of these results could be incorporated into one theory. The 1960 Bonn notes of Thom and Harold Levine (reprinted in [42]) gave the first general exposition of this theory. However, these notes preceded the work of Bernard Malgrange [23] on what is now known as the Malgrange Preparation Theorem-which allows the relatively easy computation of normal forms of stable singularities as well as the proof of the main theorem in the subject-and the definitive work of John Mather. More recently, two survey articles have appeared, by Arnold [4] and Wall [53], which have done much to codify the new material; still there is no totally accessible description of this subject for the beginning student. We hope that these notes will partially fill this gap. In writing this manuscript, we have repeatedly cribbed from the sources mentioned above-in particular, the Thom-Levine notes and the six basic papers by Mather |
| Beschreibung: | 1 Online-Ressource (209p) |
| ISBN: | 9781461579045 9780387900735 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4615-7904-5 |
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Datensatz im Suchindex
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| any_adam_object | |
| author | Golubitsky, Martin |
| author_facet | Golubitsky, Martin |
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| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4615-7904-5 |
| format | Electronic eBook |
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| id | DE-604.BV042420951 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:08Z |
| institution | BVB |
| isbn | 9781461579045 9780387900735 |
| issn | 0072-5285 |
| language | English |
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| spelling | Golubitsky, Martin Verfasser aut Stable Mappings and Their Singularities by Martin Golubitsky, Victor Guillemin New York, NY Springer US 1973 1 Online-Ressource (209p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 14 0072-5285 This book aims to present to first and second year graduate students a beautiful and relatively accessible field of mathematics-the theory of singu larities of stable differentiable mappings. The study of stable singularities is based on the now classical theories of Hassler Whitney, who determined the generic singularities (or lack of them) of Rn ~ Rm (m ~ 2n - 1) and R2 ~ R2, and Marston Morse, for mappings who studied these singularities for Rn ~ R. It was Rene Thorn who noticed (in the late '50's) that all of these results could be incorporated into one theory. The 1960 Bonn notes of Thom and Harold Levine (reprinted in [42]) gave the first general exposition of this theory. However, these notes preceded the work of Bernard Malgrange [23] on what is now known as the Malgrange Preparation Theorem-which allows the relatively easy computation of normal forms of stable singularities as well as the proof of the main theorem in the subject-and the definitive work of John Mather. More recently, two survey articles have appeared, by Arnold [4] and Wall [53], which have done much to codify the new material; still there is no totally accessible description of this subject for the beginning student. We hope that these notes will partially fill this gap. In writing this manuscript, we have repeatedly cribbed from the sources mentioned above-in particular, the Thom-Levine notes and the six basic papers by Mather Mathematics Mathematics, general Mathematik Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Stabilitätstheorie Logik (DE-588)4433824-7 gnd rswk-swf Abbildung Mathematik (DE-588)4000044-8 gnd rswk-swf Singularität Mathematik (DE-588)4077459-4 gnd rswk-swf Differenzierbare Abbildung (DE-588)4149802-1 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 s Abbildung Mathematik (DE-588)4000044-8 s 1\p DE-604 Differenzierbare Abbildung (DE-588)4149802-1 s Singularität Mathematik (DE-588)4077459-4 s 2\p DE-604 Stabilitätstheorie Logik (DE-588)4433824-7 s 3\p DE-604 Guillemin, Victor Sonstige oth https://doi.org/10.1007/978-1-4615-7904-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Golubitsky, Martin Stable Mappings and Their Singularities Mathematics Mathematics, general Mathematik Funktionentheorie (DE-588)4018935-1 gnd Stabilitätstheorie Logik (DE-588)4433824-7 gnd Abbildung Mathematik (DE-588)4000044-8 gnd Singularität Mathematik (DE-588)4077459-4 gnd Differenzierbare Abbildung (DE-588)4149802-1 gnd |
| subject_GND | (DE-588)4018935-1 (DE-588)4433824-7 (DE-588)4000044-8 (DE-588)4077459-4 (DE-588)4149802-1 |
| title | Stable Mappings and Their Singularities |
| title_auth | Stable Mappings and Their Singularities |
| title_exact_search | Stable Mappings and Their Singularities |
| title_full | Stable Mappings and Their Singularities by Martin Golubitsky, Victor Guillemin |
| title_fullStr | Stable Mappings and Their Singularities by Martin Golubitsky, Victor Guillemin |
| title_full_unstemmed | Stable Mappings and Their Singularities by Martin Golubitsky, Victor Guillemin |
| title_short | Stable Mappings and Their Singularities |
| title_sort | stable mappings and their singularities |
| topic | Mathematics Mathematics, general Mathematik Funktionentheorie (DE-588)4018935-1 gnd Stabilitätstheorie Logik (DE-588)4433824-7 gnd Abbildung Mathematik (DE-588)4000044-8 gnd Singularität Mathematik (DE-588)4077459-4 gnd Differenzierbare Abbildung (DE-588)4149802-1 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Funktionentheorie Stabilitätstheorie Logik Abbildung Mathematik Singularität Mathematik Differenzierbare Abbildung |
| url | https://doi.org/10.1007/978-1-4615-7904-5 |
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